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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p><dfn class="terminology">Theorem</dfn> Suppose that <span class="process-math">\(y_1\)</span> and <span class="process-math">\(y_2\)</span> are two solutions of</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq3_5_4.html">
\begin{equation*}
y^{\prime \prime}+p(x) y^{\prime}+q(x) y=0.
\end{equation*}
</div>
<p class="continuation">If there is a point <span class="process-math">\(x_0\)</span> such that</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq3_5_4.html">
\begin{equation}
W(y_1, y_2)|_{x=x_0}\neq 0\tag{3.2.1}
\end{equation}
</div>
<p class="continuation">then</p>
<div class="displaymath process-math" data-contains-math-knowls="./knowl/eq3_5_4.html">
\begin{equation*}
y=C_1 y_1(x)+C_2 y_2(x)
\end{equation*}
</div>
<p class="continuation">is the general solution. If (<a href="" class="xref" data-knowl="./knowl/eq3_5_4.html" title="Equation 3.2.1">(3.2.1)</a>) is satisfied, we call <span class="process-math">\(y_1\)</span> and <span class="process-math">\(y_2\)</span> form <dfn class="terminology">a fundamental set of solutions</dfn>.</p>
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